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The search function in OmniFocus is really a filter for whatever view you are in. To search the entire library, you need to be in a view (e.g.: select the Library in Planning Mode, view filter set to remaining or any status) to find tasks across the library.

I don't use Evernote myself, so I cannot say one way or the other. Users either like the filter in OmniFocus or would like to see a global search. Personally, I prefer the filter option. The way it works now, I can be focused on a project or an area folder and filter for a search term that only appears in the focus. That prevents tasks from outside the focus from grabbing my attention when I don't need the distraction-very consistent with GTD.

For some alternatives to the built-in search, you might want to look in the OmniFocus Extras forum for some scripts that are global. In particular, member RobTrew has shared some excellent scripts to get the most from OmniFocus.